Jun 22 2010

## Subatomic Particle Structure

Research on the internal structure of subatomic particles has been ongoing since the early days of particle accelerators and cosmic ray experiments, and there are several points of view that merit study. The view promoted here has not much new, and should sound familiar. The very stable proton, as CERN would agree, is a worthy starting point.

First of all, “there is *no hard core* to the proton. … It could be like jelly, or it could be like a strawberry, with seeds scattered throughout, but *no accumulation* of them at the centre.” When scattering e^{–} + p is elastic, the resulting Bjorken scaling “is interpreted as indicating that the scattering takes place off point like constituents of the proton, called partons.”, where “the structure factors are functions of ω only.” ([1], pgs 16-18).

Since “q is the photon 4-momentum”, for “an individual parton of mass m” we can use the relativistic mass of the graviton, m_{g} = 5.575 x 10^{-28} kg [2], in which case the dimensionless ω = (2Mν)/q^{2}, with q^{2} = 2mν ([1], pg 17), gives ω = m_{p}/m_{g} = 3.

One may think of the internal structure of the proton as a crystal lattice, with nodes, or partons, that are basically zero points of eigenvectors, where internal and pass through wave functions add or subtract momentum. If you are a string theorist, added head to tail you may choose to look at the vector structure as vibrating strings. If you have a Mechanical or Civil engineering degree you may think of the structure as finite elements, – not necessarily tetrahedral however. The nodes are the seeds of Ryder’s strawberry.

The defined boundary of a subatomic particle results from gravitational pressure at its barrier domain. Let us view then the particle as a wave packet “when the wave packet is subject to the influence of a parabolic potential. Physically, this result arises from the fact that the tendency of the wave packet to spread is compensated by the potential, whose effect is to push the wave packet towards the origin from regions where V(x) is large.” ([3], Compl. G_{v}, 3.c., pg 572) Due to gravitational pressure, V(x) would be large at the barrier domain of the particle. With consistent frequency, ω_{g} = 4.75 x 10^{23} rad. sec^{-1} [2], gravitons step through the barrier easily.

Baryons and fermions would be similar in structure, though differing greatly in density. Scattering can happen through barrier elasticity or partial penetration with node to node scattering. Deeper node penetration on a large nucleus can result in alpha decay.

[1] Ryder, Lewis H., Quantum Field Theory, Second Edition, Cambridge University Press, 1996

[2] http://www.fruechtetheory.com/blog/2010/06/15/muonic-states/

[3] Cohen-Tannoudji, Dui, Laloë, Quantum Mechanics, Hermann, 1977, Paris, France